A REFLEXIVITY THEOREM FOR SUBSPACES OF CALKIN ALGEBRAS

A linear subspace J of an algebra G is called reflexive if a is-an-element-of J whenever a is-an-element-of G and paq = 0 for every pair p, q of indempotents in G such that pJq = {0}. This paper studies properties of a Banach space that ensure that every separable norm closed linear subspace of the corrsponding Calkin algebra is reflexive. The latter holds for the spaces c0 and l(p), 1 < p < infinity. (C) 1994 Academic Press, Inc.